If you just save the html thread, all you see is the "display text" for the links, which doesn't directly give you the URL (and thread number) for the links. You still have to go through them one at a time to extract the thread numbers.
With the "print table of links" feature, if your printer offers it, you get a full printout of the actual URLs, including as part of the URLs a list of the thread numbers (if you can read the URLs). Since Joe suggested trying to figure out how to use the thread numbers, the "print links" is the easiest way to capture them all.